The equation of the given circle is [tex](x-6)^{2}+(y+9)^{2}=100.[/tex]
Step-by-step explanation:
Step 1:
The equation of a circle with its center at (h, k) and a radius of r is given by
[tex](x-h)^{2}+(y-k)^{2}=r^{2}.[/tex]
The h value is the x coordinate and the k value is the y coordinates, so (h, k) is (6, -9).
The radius is given as 10 so [tex]r =10[/tex] and [tex]r^{2} = 100.[/tex]
Step 2:
By substituting the values we know, we get
[tex](x-h)^{2}+(y-k)^{2}=r^{2} = (x-6)^{2}+(y-(-9))^{2}=10^{2}.[/tex]
So the equation of the given circle is
[tex](x-6)^{2}+(y+9)^{2}=100.[/tex]
